Control of dispersion is desirable in many optical applications, such as compensation for fiber-induced dispersion in communications systems, tunable group-velocity dispersion for mode locking of laser sources, and quantum scrambling for quantum enigma machines. Conventional techniques for controlling dispersion include chirped fiber gratings, coupled resonator optical waveguides (CROWs), and side-coupled integrated spaced sequences of resonators (SCISSORs). However, as interest turns towards dispersion-based quantum applications, dispersion control with a large number of tunable parameters becomes desirable to enable a large set of basis states. For these applications, conventional solutions usually are not able to provide the desired tunability, speeds, and scalability for practical demonstrations.
For example, a quantum enigma machine can be constructed based on quantum data locking. Suppose that a sender (usually referred to as Alice) possesses an n-bit message j that she wishes to send to a receiver (usually referred to as Bob). Alice and Bob initially possess a secret, fully random m-bit string k (also referred to as the seed), where m<<n. They publicly agree upon a set of 2m unitary operations Uk, randomly selected according to the Haar measure. Alice first maps the message j to a quantum state |j. She then applies the transformation Uk corresponding to the shared seed k and sends the resulting state |jk=Uk|j to Bob. Bob decodes the message by applying the inverse transformation Uk−1|jk=|j. The devices that perform Alice's and Bob's encoding and decoding operations can be termed quantum enigma machines, in analogy to classical enigma machines that encode and decode via classical invertible transformations.
Although quantum data locking may be realized in theory using bulk optical components, scaling to larger mode numbers (larger dimensionality) involves a degree of phase stability and device complexity that is difficult to realize using bulk optics. In addition, it is also desirable in quantum data locking to realize various operations Uk using the same hardware device (e.g., transmitter and/or receiver) so as to scramble the input in various ways. This broad tunability is also a challenge for bulk optics.